Question

15 балов за несложное задание
Обчисліть значення виразу.

Answer 1

$1) \ \sqrt[5]{16} \ \cdotp \sqrt[5]{2} =\sqrt[5]{16 \ \cdotp 2} =\sqrt[5]{32} = 2\\\\2) \ \sqrt[6]{10000} \ \cdotp \sqrt[6]{100} = \sqrt[6]{10^{4}} \ \cdotp \sqrt[6]{10^{2}} = \sqrt[6]{10^{4} \ \cdotp 10^{2}} = \sqrt[6]{10^{6}} = 10 \\\\3) \ \sqrt[3]{0,108} \ \cdotp \sqrt[3]{2} = \sqrt[3]{0,108 \ \cdotp 2} = \sqrt[3]{0,216} = 0,6$

$4) \ \sqrt[8]{3^{5} \ \cdotp 5^{2}} \ \cdotp \sqrt[8]{3^{3} \ \cdotp 5^{6}} = \sqrt[8]{3^{5} \ \cdotp 5^{2} \ \cdotp 3^{3} \ \cdotp 5^{6}} = \sqrt[8]{3^{8} \ \cdotp 5^{8}} = 3 \ \cdotp 5 = 15 \\\\5) \ \dfrac{\sqrt[5]{96}}{\sqrt[5]{729}} = \sqrt[5]{\dfrac{96}{729}} = \sqrt[5]{\dfrac{32}{243}} = \dfrac{2}{3}$

$6) \ \dfrac{\sqrt[3]{5^{8} \ \cdotp 7^{10}}}{\sqrt[3]{5^{2} \ \cdotp 7^{16}}} = \sqrt[3]{ \dfrac{5^{8} \ \cdotp 7^{10}}{5^{2} \ \cdotp 7^{16}}} = \sqrt[3]{\dfrac{5^{6}}{7^{6}}} = \dfrac{5^{2}}{7^{2}} = \dfrac{25}{49} \\\\7) \ \sqrt[3]{5 - \sqrt{17}} \ \cdotp \sqrt[3]{5 + \sqrt{17}} = \sqrt[3]{(5 - \sqrt{17})(5 + \sqrt{17})} = \sqrt[3]{25 - 17} = \sqrt[3]{8} = 2$

$8) \ \sqrt[4]{26 + \sqrt{51}} \ \cdotp \sqrt[4]{26 - \sqrt{51}} = \sqrt[4]{(26 + \sqrt{51})(26 - \sqrt{51})} = \sqrt[4]{676 - 51} = \sqrt[4]{625} = 5$

$9) \ \sqrt[5]{3\sqrt{2} - 5\sqrt{2}} \ \cdotp \sqrt[5]{3\sqrt{2} + 5\sqrt{2}} = \sqrt[5]{(3\sqrt{2} - 5\sqrt{2})(3\sqrt{2} + 5\sqrt{2})} = \sqrt[5]{(-2\sqrt{2}) \ \cdotp 8\sqrt{2}} = \sqrt[5]{-32} = -2$